New experimental techniques give a more detailed picture of the lateral motion of cell membrane components than was previously available. In single-particle tracking (SPT), computer-enhanced video microscopy is used to measure the trajectories of labeled individual membrane proteins at a spatial resolution of tens of nanometers and a time resolution of tens of milliseconds. One of the major results of SPT experiments is that a significant fraction of proteins in the cell membrane undergo various types of non-Brownian motion, including anomalous diffusion, directed motion, and confined motion. Transitions are often observed between modes of motion. In laser and magnetic tweezer experiments, piconewton forces are used to move labeled proteins within the membrane, in order to probe hindrances to motion. In this project, Monte Carlo techniques and percolation theory are used to do modeling to support these experiments and to examine the hypothesis that lateral motion in cells is to a large scale non-Brownian, and controlled by different mechanisms on different time and length scales. Three broad questions are addressed. First, how do particles move on the cell surface? The analysis of data from SPT and tweezer experiments will be examined, to develop ways to identify and characterize the various modes of motion reliably despite the high noise inherent in measurements of motion of individual microscopic particles. Second, how is the cell surface organized? Various models of hindered diffusion will be studied, to see their effect on SPT and fluorescence photobleaching recovery experiments. Third, what are the effects of heterogeneous motion in heterogeneous environments on kinetics and equilibrium? Kinetics of transmembrane signaling will be modified. Additional work will consider the effect of obstruction on three-dimensional diffusion in cytoplasm.